1 Triggers and settings

2 Import Data

Note: for Neah Bay in 2016

  1. There are not algae data for the South Area only, the North.
  2. There are are only two transects of invert data for the North. There are 5 transects in the South area.

3 By KELP SPECIES but summed across all urchins

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the `.groups` argument.

3.1 Individual plot version

The following splits the facet into individual plots for better plotting and labeling.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a  0.63882    0.16024   3.987 0.000459 ***
## k -0.06876    0.13210  -0.520 0.606977    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.692 on 27 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 7.697e-06
##   (1 observation deleted due to missingness)

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the `.groups` argument.
## `geom_smooth()` using formula 'y ~ x'

3.2 Site x Year regressions for urchins vs kelp

## 
## Call:
## lm(formula = Kelp ~ Urchins, data = nereo[nereo$site == "Tatoosh Island", 
##     ])
## 
## Residuals:
##       1       2       3       4       5       6 
## -0.9531  1.2689  0.2367 -0.3856  0.7625 -0.9294 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 1.8447189  0.7712348   2.392    0.075 .
## Urchins     0.0007168  0.0151550   0.047    0.965  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.021 on 4 degrees of freedom
## Multiple R-squared:  0.000559,   Adjusted R-squared:  -0.2493 
## F-statistic: 0.002237 on 1 and 4 DF,  p-value: 0.9645
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = nereo[nereo$site == "Destruction Island", 
##     ])
## 
## Residuals:
##        1        2        3        4        5        6 
##  0.18941 -0.19240  0.69272  0.05353  0.11054 -0.85380 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.20345    0.27457   4.383   0.0118 *
## Urchins     -0.02019    0.02478  -0.815   0.4609  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5694 on 4 degrees of freedom
## Multiple R-squared:  0.1423, Adjusted R-squared:  -0.07208 
## F-statistic: 0.6638 on 1 and 4 DF,  p-value: 0.4609
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = ptery[ptery$site == "Tatoosh Island", 
##     ])
## 
## Residuals:
##       1       2       3       4       5       6 
##  0.2926 -0.1347 -0.5921  0.2537  0.5546 -0.3740 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.410210   0.371301   1.105   0.3312  
## Urchins     0.025339   0.007296   3.473   0.0255 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4915 on 4 degrees of freedom
## Multiple R-squared:  0.7509, Adjusted R-squared:  0.6887 
## F-statistic: 12.06 on 1 and 4 DF,  p-value: 0.02552
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = ptery[ptery$site == "Destruction Island", 
##     ])
## 
## Residuals:
##        1        2        3        4        5        6 
## -0.26151  0.23442 -0.12751 -0.03642 -0.02639  0.21742 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.480561   0.104792   4.586   0.0101 *
## Urchins     -0.003854   0.009456  -0.408   0.7045  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2173 on 4 degrees of freedom
## Multiple R-squared:  0.03987,    Adjusted R-squared:  -0.2002 
## F-statistic: 0.1661 on 1 and 4 DF,  p-value: 0.7045

4 Total for each.

I know we’re not supposed to combine macro & nereo but…just to see

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site'. You can override using the `.groups` argument.

5 BY SPECIES

5.1 Transect level, all depths

## 
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggpubr':
## 
##     get_legend
## Loading required package: viridisLite

## By Site and Depth level

## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override using the `.groups` argument.
## [1] 495   7
## [1] 165   5
## [1] 165   5

correlation purple vs nereo at Tatoosh r = 0.2273737, p = 0.0950256

5.2 By Site and 5 m only

## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override using the `.groups` argument.
## [1] 495   7
## [1] 165   5
## [1] 165   5
## $x
## [1] "Urchin density"
## 
## $y
## [1] "Kelp density"
## 
## $colour
## [1] "Site"
## 
## attr(,"class")
## [1] "labels"

5.3 By site, averaged across depths, data = years

## `summarise()` has grouped output by 'year', 'site'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year', 'site'. You can override using the `.groups` argument.
## [1] 270   7
## [1] 90  4
## [1] 90  4

## [1] NA
## [1] NA

This plot compared to the previous is interesting.

  1. At the transect level, there is a negative correlation between urchin density and kelp neroycystis density at Tatoosh

  2. At the site level, there is a positive correlation for Nerocystis (r = NA) and for Pterogophora (r = NA)at Tatoosh across years.

6 TATOOSH

6.1 By transect

## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a  2.66810    0.51870   5.144 3.84e-06 ***
## k -0.11738    0.07926  -1.481    0.144    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.17 on 54 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.24e-06
##          a          k 
##  2.6681018 -0.1173773
## [1] 249.6557

7 Across years

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

8 Coastwide urchin - kelp patterns

8.1 All kelp: Nereo + Macro + Ptero

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

cor: r = 0.6439593; p = 0.1675807

8.2 Canopy only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

cor r = 0.3495239

8.3 Nero only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

8.4 Macro only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

## Ptero only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

cor r = 0.8916147; = 0.0169844

9 Tatoosh only

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a 12.73286    2.03142   6.268 6.32e-08 ***
## k -0.01436    0.01149  -1.250    0.217    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.459 on 54 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.446e-06
##           a           k 
## 12.73285884 -0.01436079
## [1] 414.5497

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can override using the `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a 4.785827   1.035885   4.620 2.42e-05 ***
## k 0.004516   0.031080   0.145    0.885    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.728 on 54 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.117e-07
##           a           k 
## 4.785826681 0.004515701
## [1] 358.3601

10 Additional supplement figure

11 Figure 6 output for main MS

## `geom_smooth()` using formula 'y ~ x'

12 Combined Figure 5

## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

13 Kelp vs Kelp

## `summarise()` has grouped output by 'site', 'year'. You can override using the `.groups` argument.

Correlations between kelps

Macro vs Nereocystis, all sites r = -0.4863198 with p = 0.0064318

Macro vs Nereocystis, two sites r = 0.2257643 with p = 0.4804755

Macro vs Pterygophora, all sites r = 0.2289692 with p = 0.2235754

Macro vs Nereocystis, all sites r = 0.1389036 with p = 0.464145

14 Correlations at Tatoosh Island across years (yearly means) for different depth zones

A different, and simplified version of the above for just tatoosh and faceted by species.

Essentially, there are different relationships at different depths. Probably too much detail for this manuscript.

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone', 'transect'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year', 'zone'. You can override using the `.groups` argument.